Japan's Daizen Maeda marked his 100th Celtic appearance with a hat-trick as the holders booked their place in the Scottish Cup semi-finals with a 4-2 win against Livingston on Saturday.

But the morale-boosting win, which followed last weekend's league defeat by Hearts, was anything but straightforward.

Bottom of the Premiership table Livingston twice came from behind to equalise through Daniel MacKay and Tete Yengi as they pressed for the club's first win at Parkhead.

From 2-2, however, Maeda went on to complete his hat-trick in the 86th minute before fellow Japan international Kyogo Furuhashi gave the final scoreline a flattering look for Celtic with a goal deep into stoppage time.

Celtic were once again without captain Callum McGregor, who hopes to return from an Achilles injury after the international break.

Hoops boss Brendan Rodgers decided to rest Cameron Carter-Vickers due to a longstanding hamstring problem that has seen the defender endure several lay-offs already this season.

Rodgers, while pleased by winger Maeda's finishing, said: "We didn't close the spaces anywhere near what we would want and the speed of our game wasn't what we would want. But I am understanding of that, some of the guys coming in and also the level of players who were missing."

Livingston manager David Martindale said he hoped his side, six points adrift at the foot of the table, would take heart from this performance.

"I'm pretty proud of them albeit we're out of the Cup," he said.

"It's been a painful season and we're on a torrid run. I don't need self-belief, but I can only hope the players take a little bit of self-belief."

Celtic's arch-rivals Rangers beat nine-man Hibernian 2-0.

John Lundstram gave League Cup winners Rangers a 23rd-minute lead when he forced in a rebound after skipper James Tavernier's penalty was saved by David Marshall.

Hibs, however, stayed in the game despite losing Martin Boyle to a worrying injury with the Australia international motionless on the Easter Road turf after John Souttar landed on him.

Following a lengthy delay, Boyle left the pitch on a stretcher before being taken to hospital.

Rangers appeared to be struggling at the start of the second half following their 2-2 draw with Benfica in the Europa League in Lisbon on Thursday.

But Hibs' Jordan Obita and Nathan Moriah-Welsh were then both sent off in the space of three minutes.

Obita was dismissed for a second bookable offence in the 68th minute after a foul on Rabbi Matondo before Moriah-Welsh was shown a straight red for a reckless challenge on Lundstram.

Hibs continued to hold out before Portuguese striker Fabio Silva's goal seven minutes from time made the game safe for the visitors.

The semi-finals will feature Celtic, Rangers, Aberdeen and the winners of Championship side Morton's match against Hearts on Monday.